Forces of ` 5 N, 12 N` and ` 13 N` are equilibrimum. If ` sin 23^@= 5 //13 `, the angle between ` 5 N` and ` 13N` force is.

Options

A. ` 23^2`
B. `67^(@)`
C. `90^@`
D. ` 113^@

Answer

D

Explanation

Since ` 13^@ =5^2 + 12 ^2` and the forces are in ewuilibrium, so they must be represented by the three sides of a right angle triangle ` OAB` as shown in Fig. 2 (CF) . 52. We have to calculate
.
` /_AOC= (180^@ - alpha).
In ` Delta AOB, sin theta = 5/(13)= sin 23^@ , so theta = 23^@`.
:. ` alpha = 90^2 - theta= 90^@ - 23^@ = 67^@`
:. ` /_AOC = 180^@ - 67^@ = 113^@`.